Non-uniform dependence of the data-to-solution map for the two-component Fornberg-Whitham system

被引：4

作者：

Yu, Yanghai ^{[1
]}

Li, Jinlu ^{[2
]}

机构：

[1] Anhui Normal Univ, Sch Math & Stat, Wuhu 241002, Peoples R China

[2] Gannan Normal Univ, Sch Math & Comp Sci, Ganzhou 341000, Peoples R China

来源：

ANNALI DI MATEMATICA PURA ED APPLICATA | 2023年 / 202卷 / 01期

基金：

中国国家自然科学基金;

关键词：

Fornberg-Whitham equation; Non-uniform dependence; Sobolev spaces; WELL-POSEDNESS; CAMASSA-HOLM; INITIAL DATA; CAUCHY-PROBLEM; ILL-POSEDNESS; EQUATION; EULER;

D O I：

10.1007/s10231-022-01232-8

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

In this paper, we consider the Cauchy problem for the two-component Fornberg-Whitham system on the real line and study the issue of uniform dependence on initial data for this equation. We prove that the solution map of this problem cannot be uniformly continuous in Sobolev spaces H-s(R) x H-s(-1)(R) for s > 3/2.

引用

页码：59 / 76

页数：18

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